/*
 * @lc app=leetcode id=36 lang=cpp
 *
 * [36] Valid Sudoku
 *
 * https://leetcode.com/problems/valid-sudoku/description/
 *
 * algorithms
 * Medium (46.49%)
 * Likes:    1273
 * Dislikes: 410
 * Total Accepted:    311.9K
 * Total Submissions: 668.8K
 * Testcase Example:  '[["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]'
 *
 * Determine if a 9x9 Sudoku board is valid. Only the filled cells need to be
 * validated according to the following rules:
 * 
 * 
 * Each row must contain the digits 1-9 without repetition.
 * Each column must contain the digits 1-9 without repetition.
 * Each of the 9 3x3 sub-boxes of the grid must contain the digits 1-9 without
 * repetition.
 * 
 * 
 * 
 * A partially filled sudoku which is valid.
 * 
 * The Sudoku board could be partially filled, where empty cells are filled
 * with the character '.'.
 * 
 * Example 1:
 * 
 * 
 * Input:
 * [
 * ⁠ ["5","3",".",".","7",".",".",".","."],
 * ⁠ ["6",".",".","1","9","5",".",".","."],
 * ⁠ [".","9","8",".",".",".",".","6","."],
 * ⁠ ["8",".",".",".","6",".",".",".","3"],
 * ⁠ ["4",".",".","8",".","3",".",".","1"],
 * ⁠ ["7",".",".",".","2",".",".",".","6"],
 * ⁠ [".","6",".",".",".",".","2","8","."],
 * ⁠ [".",".",".","4","1","9",".",".","5"],
 * ⁠ [".",".",".",".","8",".",".","7","9"]
 * ]
 * Output: true
 * 
 * 
 * Example 2:
 * 
 * 
 * Input:
 * [
 * ["8","3",".",".","7",".",".",".","."],
 * ["6",".",".","1","9","5",".",".","."],
 * [".","9","8",".",".",".",".","6","."],
 * ["8",".",".",".","6",".",".",".","3"],
 * ["4",".",".","8",".","3",".",".","1"],
 * ["7",".",".",".","2",".",".",".","6"],
 * [".","6",".",".",".",".","2","8","."],
 * [".",".",".","4","1","9",".",".","5"],
 * [".",".",".",".","8",".",".","7","9"]
 * ]
 * Output: false
 * Explanation: Same as Example 1, except with the 5 in the top left corner
 * being 
 * ⁠   modified to 8. Since there are two 8's in the top left 3x3 sub-box, it
 * is invalid.
 * 
 * 
 * Note:
 * 
 * 
 * A Sudoku board (partially filled) could be valid but is not necessarily
 * solvable.
 * Only the filled cells need to be validated according to the mentioned
 * rules.
 * The given board contain only digits 1-9 and the character '.'.
 * The given board size is always 9x9.
 * 
 * 
 */

// @lc code=start
class Solution {
public:
    bool isValidSudoku(vector<vector<char>>& board) {
        bool row[9][9] = {false};
        bool col[9][9] = {false};
        bool cell[3][3][9] = {false};

        for (int i = 0; i < 9; ++i) {
            for (int j = 0; j < 9; ++j) {
                if (board[i][j] == '.') continue;

                int t = board[i][j] - '1';
                if (row[i][t]) return false;
                if (col[t][j]) return false;
                if (cell[i / 3][j / 3][t]) return false;

                row[i][t] = true;
                col[t][j] = true;
                cell[i / 3][j / 3][t] = true;
            }
        }

        return true;
    }
};
// @lc code=end

